Question: Simplify the following expression: $z = \dfrac{t^2 + 8t + 12}{t + 6} $
Answer: First factor the polynomial in the numerator. $ t^2 + 8t + 12 = (t + 6)(t + 2) $ So we can rewrite the expression as: $z = \dfrac{(t + 6)(t + 2)}{t + 6} $ We can divide the numerator and denominator by $(t + 6)$ on condition that $t \neq -6$ Therefore $z = t + 2; t \neq -6$